1. A study is done to determine whether switching laptops to use \"buttery\"-style keyboards (where keys are almost at and sink only slightly when pressed} affects the number of words typed per minute. A pool of 1C} long-time laptop users is split at random into two groups of size n=5. One group uses a traditional keyboard for a typing exercise, and the other group carries out the same typing exercise using a buttery keyboard. The results are collected and shown below: Classic Keyboard WPM: 41, TU, 25, 53, 58 (mean 51.4, sample sd 18.23} Buttery Keyboard WPM: 3E, {52, 20, 58, 41 {mean 43.4, sample sd 17.08} (a) Carry out a two-tailed, independent samples t-test to compare the words per minute typed by the two groups. State your hypotheses and please show how to determine the t-statistic and the appropriate degrees of freedom for the t-distribution in this case (yes, using that complicated formula, just this once). You may assume the pvalue for the test is 0.4944; write up an appropriate conclusion for the test